lecture notes
Problem SetsWeekly problem sets will be posted here, starting in the first week of the semester.For general information about the course, scroll down a bit... |
![]() image by Christian Lawson-Perfect from cp's mathem-o-blog |
Instructor: Prof. Chris Wendl (for contact information and office hours see my homepage)
Moodle:
https://moodle.hu-berlin.de/course/view.php?id=133147
The enrollment key is: obstruction
Important: You must join the moodle for the course in order to receive occasional
time-sensitive announcements, e.g. if a lecture has been cancelled or rescheduled.
HU students can access moodle using their HU username and password.
Non-HU users can access it by following this link
and then clicking on "Create new account".
You will need to enter the enrollment key printed above.
Time and place:
Lectures on Wednesdays and Thursdays 11:15-12:45 in room 1.012 (RUD25)
Problem Class (Übung) Wednesdays 13:15-14:45 in room 1.012 (RUD25)
Note: We may adjust the Wednesday schedule a bit in order
to allow for a more comfortable lunch between lecture and problem class.
This will be discussed and decided in the first lecture.
Language:
The course will be taught in English.
Prerequisites:
The main prerequisites are a solid foundation in point-set topology,
the fundamental group and covering spaces, singular and cellular (co-)homology
(including computations based on the axioms and some homological algebra,
e.g. the universal coefficient theorems), and some willingness to put up with the
language of categories, functors and universal properties. If you have taken my
Topologie II course before,
then you definitely have the essential prerequisites, but you probably also have
them if you learned about homology and cohomology elsewhere.
Some knowledge of smooth manifolds will occasionally be useful, but if you do not
have this, you will just need to be willing to accept a small set of facts about
tangent spaces, tubular neighborhoods and transversality as black boxes.
Contents:
This is a course on intermediate-level algebraic topology, and
is conceived in part as a sequel to
last semester's Topology 2 course.
We aim to prove some useful results from
elementary homotopy theory (some of which were mentioned briefly last semester
but were not proved), and introduce the essentials of obstruction theory,
classifying spaces, characteristic classes, and bordism theory.
These are all topics that have wide-ranging applications to other areas
of mathematics, especially to problems in differential geometry and topology,
such as the existence and classification of exotic smooth structures
on manifolds. We will not attempt any deep exploration of modern
homotopy theory, as that would far exceed my expertise.
Here is a more detailed plan of topics, though I cannot promise that all of them will be covered.
Literature:
The top of this page contains a link to detailed lecture notes for this
course which will be updated routinely as the course progresses.
The bulk of what we plan to cover is in any case contained in the union of the
following three books:
Homework:
Weekly problem sets will be posted near the top of this page, and some
subset of those problems will be discussed in the problem class
(Übung) each week. Homework will not be collected or graded.
The problem class may sometimes also be used
to fill in gaps on details that did not fit into the regular lectures.
Grades:
Since this is an advanced course, I have a fairly relaxed attitude about
grades. If you come to the course with adequate prerequisites and stay with
it for the whole semester, you can come to my office at the end
for a conversation (let's pretend that's the English translation of
“mündliche Prüfung”). The format is as follows:
you pick one particular coherent topic from the course to focus on, typically the contents
of four to six lectures, and we will talk about that.
If you demonstrate that you learned something
interesting from the course, you'll get a good grade.